Yes you totally can i have installed aftermarket horn in my alto without any wire alteration
You need a wire, connect a thimble on side, female spade on the other side.
I dont have a specific idea about Honda connector but toyota and suzuki have same connectors.
The original connector plugs to one male spade pin of aftermarket horn. The other new connector you have made will connect (female spade) side to make spade pin on horn and then thimble on the bolt that holds the horn as ground
if you can share Honda City specific connector i can guide you better, on which parts to buy and how to make your own connector